Influence of rotation on the (m,n)=(3,2) neoclassical tearing mode threshold in ASDEX Upgrade S. Fietz , M. Maraschek, H. Zohm, M. Reich, L. Barrera, R. M. McDermott and the ASDEX Upgrade Team Max Planck Institute for Plasma Physics, EURATOM Association , Garching, Germany E-mail: [email protected]Abstract. The influence of rotation on the (m,n)=(3,2) neoclassical tearing mode onset and the marginal point at ASDEX Upgrade is investigated. In this context the different trigger mechanisms have been identified and the influence of not only the rotation but also the rotation gradient and the differential rotation between the resonant and the triggering surface on the NTM stability has been analysed. The existence of an upper NTM onset threshold can be observed in correlation with the rotation normalised to the Alfv´ en velocity. It can also clearly be verified that at ASDEX Upgrade the NTM onset threshold increases with co- and counter-current directed rotation and also with positive and negative rotation gradient. Submitted to: Plasma Phys. Control. Fusion
14
Embed
Influence of rotation on the (m n)=(3,2) neoclassical ...pubman.mpdl.mpg.de/pubman/item/escidoc:2144888:1/component/escidoc:...Influence of rotation on the (m,n)=(3,2) neoclassical
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Influence of rotation on the (m,n)=(3,2) neoclassical
tearing mode threshold in ASDEX Upgrade
S. Fietz, M. Maraschek, H. Zohm, M. Reich, L. Barrera, R. M.
McDermott and the ASDEX Upgrade Team
Max Planck Institute for Plasma Physics, EURATOM Association , Garching,
Abstract. The influence of rotation on the (m,n)=(3,2) neoclassical tearing mode
onset and the marginal point at ASDEX Upgrade is investigated. In this context
the different trigger mechanisms have been identified and the influence of not only
the rotation but also the rotation gradient and the differential rotation between the
resonant and the triggering surface on the NTM stability has been analysed. The
existence of an upper NTM onset threshold can be observed in correlation with the
rotation normalised to the Alfven velocity. It can also clearly be verified that at
ASDEX Upgrade the NTM onset threshold increases with co- and counter-current
directed rotation and also with positive and negative rotation gradient.
Submitted to: Plasma Phys. Control. Fusion
Influence of rotation on the (m,n)=(3,2) NTM threshold in ASDEX Upgrade 2
1. Introduction
Neoclassical tearing modes (NTMs) are resistive MHD-instabilities. They are driven
by a loss of helical bootstrap current which is caused by a flattening of the pressure
profile across the magnetic island due to enhanced transport around the island. Once
a seed island of sufficient size is generated this mechanism reinforces itself and the
NTM grows. In present devices the occurrence of NTMs degrades the confinement
and limits the maximal achievable β ( <p>B2/2µ0
). NTMs can decrease the plasma rotation
and can even lead to disruptions in particular at low q95. In large devices like ITER
NTMs are likely to be performance limiting if they are not mitigated or avoided. To
be able to control NTMs it is necessary to extrapolate the present understanding to
larger devices with different conditions. A key parameter for the NTM physics and
extrapolation is the rotation dependence. Compared to present devices, which typically
have substantial rotation, ITER will be operated at low plasma rotation due to a low
applied torque compared to the plasma inertia. With these differences the question
arises how the NTM behaviour changes with rotation and if predictions can be made
from present understanding. In addition to this, the general dependence of NTMs on
different plasma parameters, especially the understanding of the seeding mechanism and
the dependences at the NTM onset are an essential part for the control and avoidance of
NTMs. Therefore, in the following, we want to address the question of how the plasma
rotation influences the onset and the trigger process of NTMs. There exist several
possibilities how plasma rotation can influence the NTM behaviour.
It has been proposed that changes in rotation or rotation shear can reduce the normally
stabilising effect of the classical tearing stability index ∆′ [1].
Rotation can also influence the stability of NTMs by means of small island effects. The
ion polarisation current for example can be influenced by changes of the mode rotation
in the plasma frame [2] [3].
A further important issue is the effect of rotation on the trigger mechanism. On one
hand, the trigger instability itself can depend on plasma rotation as already found for
the sawtooth instability [4] [5], on the other hand the seeding process due to magnetic
coupling can be influenced by the differential rotation between the two resonant surfaces
[6].
Finally, rotation can influence the island stability due to changes of the impact of error
fields on the island or due to changes in the interaction between the island and the vessel
wall. Changes in the island structure due to rotation are also possible.
Studies concerning the rotation dependence of NTMs have already been done at DIII-D
[7], NSTX [8], JET[9] and other devices. At DIII-D experiments with co and counter
injected beam torque were done. At NSTX only co-rotation data are available, which
were obtained from experiments where the plasma rotation was varied via different
co-injected beam torques and with an externally applied error field which acts as a
drag on the plasma rotation. In both devices it was found that with decreasing co-
rotation or rotation shear the NTM onset threshold decreases and that the role of
Influence of rotation on the (m,n)=(3,2) NTM threshold in ASDEX Upgrade 3
rotation shear on the NTM stability is more important than that of rotation alone.
At DIII-D the NTM onset threshold decreases further with increasing counter-rotation.
Similarly, for decreasing rotation shear, the onset threshold decreases continuously also
when entering the region of negative shear, which is related to counter-rotation. This
raised the question of whether a sign effect is responsible for the different behaviour with
co- and counter-rotation or if the minimum onset threshold is shifted towards negative
rotation which would indicate that an ”offset” exists which is caused by diamagnetic
drifts [1]. If this is the case, then it is possible that this minimum in rotation has not
been reached yet at DIII-D and even stronger counter-current rotation data are needed
to cross this minimum. Further, in[7] and [8] it was already shown that rotation has no
influence on the ion polarisation current. Results from DIII-D and NSTX suggest that
there exists an influence of rotation or rotation shear on the underlying tearing stability
(∆′) which then is responsible for the rotation dependence of the NTM onset threshold
[7] [1].
In the following we present the corresponding results from ASDEX Upgrade for the (3,2)
NTM onset which differ in some respects from those at DIII-D and NSTX.
2. Definitions and experimental approach
The growth of an NTM can be described by the modified Rutherford equation [10]
[11] for the island width W , with rres the radius of the rational surface and τres =
µ0r2res/(1.22η) the resistive time-scale:
τresrres
dW
dt= rres∆
′(W )
+rres2µ0Lq
Bpol
δjBSabs
(
W
W 2 +W 20
+W
W 2 + 0.7w2b
)
(1)
− apolrresβpol
(
ρθiLq
Lp
)2
g(ǫ, νii)1
W 3
The parameter ǫ = rres/R0 is the inverse aspect ratio at the resonant surface,
ρθi =√
2mikBTi/eBpol is the ion poloidal gyro radius and βpol is defined as 2µ0p/B2pol
with p the total pressure and Bpol the flux surface averaged poloidal magnetic field
strength at the resonant surface. The magnetic shear length is defined as Lq = q/q′whereas the gradient length of the pressure is Lp = −p/p′ due to the normally negative
pressure gradients. The coefficients abs and apol are of the order of unity.
Beside the classical tearing stability index ∆′ in equation 1 the destabilising effect of the
bootstrap current [12], [13] is included (second term on the right hand side). A simple
and commonly used expression for the perturbation of the bootstrap current inside an
island is δjBS ≈ −ǫ 1
2∇p/Bpol [14]. A more accurate one is given by the formula in [15]:
δjBS,Sauter = I(ψ)pe
[
(−0.5) ppe
∂ ln p∂ψ
+ 0.2∂ lnTe
∂ψ+ (−0.25)∂ lnTi
∂ψ
]
√< B2 >
(2)
Influence of rotation on the (m,n)=(3,2) NTM threshold in ASDEX Upgrade 4
with ψ the poloidal flux and I(ψ) = RBtor, where R is the major radius and Btor
the toroidal magnetic field. The parameters p, pe, Te and Ti present the total pressure,
electron pressure and electron and ion temperature, respectively.
For an island size smaller than W0 the destabilising effect of the bootstrap current
is reduced due to a finite heat transport across the island which leads to incomplete
pressure flattening inside the island [16]. For W ∼ wb, which is often the case at
the onset of NTMs, finite banana width effects have to be taken into account which
additionally reduce the neoclassical drive [17] (wb is the ion banana width).
In this context an NTM drive can be defined as µ0LqδjBS/Bpol according to [8]. At
ASDEX Upgrade the q profile measurements are insufficient to reliably detect changes
in dq/dr. For this reason the dependences on q(r) are not included in all following
definitions (meaning Lq=constant).
The third term in equation 1 corresponds to the ion polarisation current, which is also
stabilising and important for small island widths [18]. This current is induced by the
propagation of the island in the plasma frame. The ion polarisation current strongly
depends on the ion collision frequency νii [19].
This dependence is included through the factor g(ǫ, νii) which is ǫ3
2 for ‘collisionless’
plasmas (νii/mǫω∗
e ¡¡1 and equal to 1 in the ‘collisional’ case (ω∗
e is the electron
diamagnetic drift frequency). In equation 1 the stabilising effects of toroidicity and
shaping [20] and further small island effects are not taken into account. The stabilising
small island effects are responsible for the need of a trigger mechanism which induces a
seed island at the resonant surface. Except for the ion polarisation current, which is not
responsible for the rotation dependence at the mode onset as already mentioned and
discussed in [7] [1], no explicit rotation dependence is included in equation 1.
In the experimental analysis, we distinguish between different trigger mechanisms which,
due to magnetic coupling, induce a seed island at the resonant surface. In figure 1 three
example discharges are presented to illustrate the determination of the onset point and
the corresponding seeding mechanisms for the following investigations. These (3,2)
NTMs are triggered by a fishbone, a sawtooth and an ELM crash. Each onset point
is clearly correlated with a distinct trigger mechanism. For most of the discharges the
trigger mechanism could be identified unmistakably as either an ELM, a fishbone or
a sawtooth crash. Cases, where the mode grows without any visible trigger, possibly
destabilised by the Te gradient, are also common. For some NTM onsets (1,1) activity
was observed but the trigger mechanism could not be specified. In cases where at the
mode onset multiple events took place the trigger mechanism is labelled as ‘unclear’.
For some islands also the marginal point could be determined. During the decay phase
of stored energy and hence the βpol, e.g. due to ramping down of the heating power, also
the island width decreases. At the marginal point the island width evolution decouples
from βpol and decays away rapidly. This is illustrated for one special case in figure 2.
For simplicity in this investigation we used the time evolution of the global βpol and not
the local one at the resonant surface like in all other analyses.
Influence of rotation on the (m,n)=(3,2) NTM threshold in ASDEX Upgrade 5
2.0
2.2
2.4
2.6
2.8
-4
-2
0
2
4
2
3
4
5
2.00 2.05 2.10 2.15 2.20time [s]
0
10
20
30
40
βN
dB
/ d
t [a
.u.]
central SXR chanel
f [k
Hz]
!shbones
NTM onset
# 27861
3/2
0.5
0.6
0.7
0.8
0.9
1.0
-4
-2
0
2
4
1.01.21.41.61.82.02.2
4.42 4.44 4.46 4.48
0
10
20
30
40
time [s]
βN
dB
/ d
t [a
.u.]
f [k
Hz]
(3/2) NTM onset
# 27834T
e [
ke
V]
3/22/1
sawtooth crash
0.00.20.40.60.81.01.21.4
-4
-2
0
2
4
-1.0-0.50.00.51.01.5
3.46 3.48 3.50 3.52 3.54 3.56 3.580
10
20
30
40
time [s]
βN
dB
/ d
t [a
.u.]
f [k
Hz]
NTM onset
# 27837
3/2
ELM crash
EL
M m
on
ito
r
a) b) c)
(2/1) NTM onset
Figure 1. (3,2) Neoclassical tearing modes at ASDEX Upgrade triggered by a) a
sawtooth crash b) a fishbone and c) an ELM with corresponding typical time-traces
to illustrate the onset evaluation and trigger correlation
10
20
30
1.2 1.3 1.4 1.5 time [s]
0.00
0.05
0.10
0.15
0.20 W (a. u.) ~ √B
~ βpol
marginal point
f [k
Hz]
# 28284
3/2
Figure 2. Illustration of the marginal point determination of a (3,2) Neoclassical
tearing mode by the decoupling of the βpol and the island width evolution
Influence of rotation on the (m,n)=(3,2) NTM threshold in ASDEX Upgrade 6
At ASDEX Upgrade the (m,n)=(3,2) NTM is the most common and hence a large
data set of (3,2) NTM onset points with a wide range of plasma rotation is available. To
extend the database, especially in the low rotation regime and with counter-rotation,
dedicated experiments have been carried out. In these experiments the plasma rotation
was varied by using different heating mixes. Two wave heating methods, ECRH (electron